feat(kernel): add telescope instantiate procedure

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

src/kernel/context.h

@@ -11,8 +11,8 @@ Author: Leonardo de Moura
 #include "kernel/expr.h"
 
 namespace lean {
+// Remark: in a nonempty context C, variable 0 is head(C)
 typedef list<binder> context;
-typedef context      telescope;
 inline context extend(context const & c, name const & n, expr const & t) { return cons(binder(n, t), c); }
 inline context extend(context const & c, binder const & b) { return cons(b, c); }
 binder const & lookup(context const & c, unsigned i);

src/kernel/expr.h

@@ -249,8 +249,12 @@ public:
     name const & get_name() const { return m_name; }
     expr const & get_type() const { return m_type; }
     binder_info const & get_info() const { return m_info; }
+    binder update_type(expr const & t) const { return binder(m_name, t, m_info); }
 };
 
+// Remark: in a telescope T, variable 0 is the last element of the list, and head(T) is variable #(length(T) - 1)
+typedef list<binder> telescope;
+
 /** \brief Lambda and Pi expressions */
 class expr_binding : public expr_composite {
     binder           m_binder;

src/kernel/instantiate.cpp

@@ -40,6 +40,17 @@ expr instantiate(expr const & e, std::initializer_list<expr> const & l) {  retur
 expr instantiate(expr const & e, unsigned i, expr const & s) { return instantiate(e, i, 1, &s); }
 expr instantiate(expr const & e, expr const & s) { return instantiate(e, 0, s); }
 
+telescope instantiate(telescope const & t, unsigned i, expr const & s) {
+    if (is_nil(t)) {
+        return t;
+    } else {
+        binder const & b = head(t);
+        return telescope(b.update_type(instantiate(b.get_type(), i, s)),
+                         instantiate(tail(t), i+1, s));
+    }
+}
+telescope instantiate(telescope const & t, expr const & s) { return instantiate(t, s); }
+
 bool is_head_beta(expr const & t) {
     expr const * it = &t;
     while (is_app(*it)) {

src/kernel/instantiate.h

@@ -18,6 +18,11 @@ expr instantiate(expr const & e, unsigned i, expr const & s);
 /** \brief Replace free variable \c 0 with \c s in \c e. */
 expr instantiate(expr const & e, expr const & s);
 
+/** \brief Replace free variable \c i with \c s in the telescope t. */
+telescope instantiate(telescope const & t, unsigned i, expr const & s);
+/** \brief Replace free variable \c 0 with \c s in the telescope t. */
+telescope instantiate(telescope const & t, expr const & s);
+
 expr apply_beta(expr f, unsigned num_args, expr const * args);
 bool is_head_beta(expr const & t);
 expr head_beta_reduce(expr const & t);